Certainly! Let's walk through the problem step-by-step to find out how much cloth each person receives when [tex]\( \frac{2}{3} \)[/tex] meters of cloth is shared equally among 10 people.
1. Determine the Total Amount of Cloth:
The problem states that the total amount of cloth available is [tex]\( \frac{2}{3} \)[/tex] meters.
2. Determine the Number of People Sharing the Cloth:
It is also given that there are 10 people sharing the cloth.
3. Calculate the Length of Cloth Received by Each Person:
To find out how much cloth each person gets, we need to divide the total amount of cloth by the number of people. This is done by dividing [tex]\( \frac{2}{3} \)[/tex] meters by 10.
4. Perform the Division:
[tex]\[
\frac{\frac{2}{3}}{10} = \frac{2}{3} \times \frac{1}{10} = \frac{2 \times 1}{3 \times 10} = \frac{2}{30} = \frac{1}{15}
\][/tex]
Therefore, each person receives [tex]\( \frac{1}{15} \)[/tex] meters of cloth.
5. Convert the Fraction to Decimal Form (Optional):
If needed, we can also express [tex]\( \frac{1}{15} \)[/tex] in decimal form.
[tex]\[
\frac{1}{15} \approx 0.06666666666666667
\][/tex]
So, when [tex]\( \frac{2}{3} \)[/tex] meters of cloth is equally distributed among 10 people, each person will receive [tex]\( \frac{1}{15} \)[/tex] meters, which is approximately [tex]\( 0.06667 \)[/tex] meters.
